遗传人工神经网络Python实现

遗传人工神经网络Python实现

介绍

人工神经网络的灵感来自我们的大脑。遗传算法受到进化的启发。本文提出了一种新型的辅助训练的神经网络:遗传神经网络。这些神经网络具有适应度等特性,并使用遗传算法训练随机生成的权重。遗传优化发生在任何形式的反向传播之前,以给梯度下降提供一个更好的起点。

序列神经网络

序列神经网络接受一个输入矩阵,在模型外部与一个真实输出值的向量配对。然后通过遍历每一层,通过权重和激活函数来变换矩阵。

遗传人工神经网络Python实现

这是一个序列神经网络,具有一个输入矩阵,两个隐藏层,一个输出层,三个权重矩阵和一种激活函数。

训练算法

最初的预测很可能是不准确的,所以为了训练一个序列神经网络做出更好的预测,我们把它看作一个复合函数。

遗传人工神经网络Python实现

创建一个损失函数,输入矩阵和真实输出向量(X和y)保持不变。

遗传人工神经网络Python实现

现在所有的东西都是关于函数的,并且有一个明确的目标(最小化损失),我们得到一个多变量微积分的优化问题。

遗传人工神经网络Python实现

随着模型显示出越来越多的复杂性,梯度下降的计算成本可能变得非常昂贵。遗传神经网络提供了一个可供选择的初始训练过程,以提供一个更好的起点,在反向传播过程中允许更少的epochs。

遗传神经网络

在遗传神经网络中,网络被视为具有fields和适应度的计算对象。这些fields被认为是在反向传播之前通过遗传算法优化的基因。这使得梯度下降具有更好的起始位置,并且允许更少的训练时间,并具有更高的模型测试准确度。考虑以下遗传神经网络,其中权重被视为计算对象中的fields。

遗传人工神经网络Python实现

这些fields是相对于遗传神经网络的每个实例的基因。就像序列神经网络一样,它可以表示为复合函数。

遗传人工神经网络Python实现

然而,在使用微积分之前,我们将使用遗传算法采取进化方法来优化权重。

遗传算法

在自然界中,染色体交叉看起来是这样的…

遗传人工神经网络Python实现

如果我们把染色体简化成块…

遗传人工神经网络Python实现

这与遗传算法用于改变权重矩阵的逻辑相同。这个想法将是创建一个初始种群的n个遗传神经网络,经过正向传播计算出一个适应度得分,最后选择最适合的个体来创建孩子。这个过程将重复,直到找到最优的初始权值进行反向传播。

应用遗传神经网络

首先,我们必须建立遗传神经网络。我们使用的是具有四个输入节点,两个隐藏层和一个输出层的训练模型(以匹配上图),这可以扩展到任何类型的神经网络。

import pandas as pd
import numpy as np
import random
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
from keras.models import Sequential
from keras.layers import Dense
# New Type of Neural Network
class GeneticNeuralNetwork(Sequential):
 # Constructor
 def __init__(self, child_weights=None):
 # Initialize Sequential Model Super Class
 super().__init__()
 # If no weights provided randomly generate them
 if child_weights is None:
 # Layers are created and randomly generated
 layer1 = Dense(4, input_shape=(4,), activation='sigmoid')
 layer2 = Dense(2, activation='sigmoid')
 layer3 = Dense(1, activation='sigmoid')
 # Layers are added to the model
 self.add(layer1)
 self.add(layer2)
 self.add(layer3)
 # If weights are provided set them within the layers
 else:
 # Set weights within the layers
 self.add(
 Dense(
 4,
 input_shape=(4,),
 activation='sigmoid',
 weights=[child_weights[0], np.zeros(4)])
 )
 self.add(
 Dense(
 2,
 activation='sigmoid',
 weights=[child_weights[1], np.zeros(2)])
 )
 self.add(
 Dense(
 1,
 activation='sigmoid',
 weights=[child_weights[2], np.zeros(1)])
 )
 # Function for forward propagating a row vector of a matrix
 def forward_propagation(self, X_train, y_train):
 # Forward propagation
 y_hat = self.predict(X_train.values)
 # Compute fitness score
 self.fitness = accuracy_score(y_train, y_hat.round())
 # Standard Backpropagation
 def compile_train(self, epochs):
 self.compile(
 optimizer='rmsprop',
 loss='binary_crossentropy',
 metrics=['accuracy']
 )
 self.fit(X_train.values, y_train.values, epochs=epochs)

遗传人工神经网络Python实现

遗传人工神经网络Python实现

现在我们已经建立了遗传神经网络,我们可以开发出一种交叉算法。我们将使用类似于上面给出的生物图示的单点交叉。每一个矩阵列都有相同的机会被选择为一个交叉点,让每一个父母组合他们的基因并将它们传递给孩子。

# Crossover traits between two Genetic Neural Networks
def dynamic_crossover(nn1, nn2):
 # Lists for respective weights
 nn1_weights = []
 nn2_weights = []
 child_weights = []
 # Get all weights from all layers in the first network
 for layer in nn1.layers:
 nn1_weights.append(layer.get_weights()[0])
 # Get all weights from all layers in the second network
 for layer in nn2.layers:
 nn2_weights.append(layer.get_weights()[0])
 # Iterate through all weights from all layers for crossover
 for i in range(0, len(nn1_weights)):
 # Get single point to split the matrix in parents based on # of cols
 split = random.randint(0, np.shape(nn1_weights[i])[1]-1)
 # Iterate through after a single point and set the remaing cols to nn_2
 for j in range(split, np.shape(nn1_weights[i])[1]-1):
 nn1_weights[i][:, j] = nn2_weights[i][:, j]
 # After crossover add weights to child
 child_weights.append(nn1_weights[i])
 # Add a chance for mutation
 mutation(child_weights)
 # Create and return child object
 child = GeneticNeuralNetwork(child_weights)
 return child

遗传人工神经网络Python实现

为了确保种群探索解空间,应该会发生突变。在这种情况下,因为解空间非常大,突变的概率显著高于大多数其他遗传算法。没有特定的方法来改变矩阵,我们在矩阵上随机执行标量乘法,幅度为2-5。

# Chance to mutate weights
def mutation(child_weights):
 # Add a chance for random mutation
 selection = random.randint(0, len(child_weights)-1)
 mut = random.uniform(0, 1)
 if mut >= .5:
 child_weights[selection] *= random.randint(2, 5)
 else:
 # No mutation
 pass

遗传人工神经网络Python实现

最后,模拟遗传神经网络的演化。我们需要网络数据来学习,因此我们将使用众所周知的 banknote机器学习数据集。

# Read Data
data = pd.read_csv('banknote.csv')
# Create Matrix of Independent Variables
X = data.drop(['Y'], axis=1)
# Create Vector of Dependent Variable
y = data['Y']
# Create a Train Test Split for Genetic Optimization
X_train, X_test, y_train, y_test = train_test_split(X, y)
# Create a List of all active GeneticNeuralNetworks
networks = []
pool = []
# Track Generations
generation = 0
# Initial Population
n = 20
# Generate n randomly weighted neural networks
for i in range(0, n):
 networks.append(GeneticNeuralNetwork())
# Cache Max Fitness
max_fitness = 0
# Max Fitness Weights
optimal_weights = []
# Evolution Loop
while max_fitness < .9:
 # Log the current generation
 generation += 1
 print('Generation: ', generation)
 # Forward propagate the neural networks to compute a fitness score
 for nn in networks:
 # Propagate to calculate fitness score
 nn.forward_propagation(X_train, y_train)
 # Add to pool after calculating fitness
 pool.append(nn)
 # Clear for propagation of next children
 networks.clear()
 # Sort based on fitness
 pool = sorted(pool, key=lambda x: x.fitness)
 pool.reverse()
 # Find Max Fitness and Log Associated Weights
 for i in range(0, len(pool)):
 # If there is a new max fitness among the population
 if pool[i].fitness > max_fitness:
 max_fitness = pool[i].fitness
 print('Max Fitness: ', max_fitness)
 # Reset optimal_weights
 optimal_weights = []
 # Iterate through all layers, get weights, and append to optimal
 for layer in pool[i].layers:
 optimal_weights.append(layer.get_weights()[0])
 print(optimal_weights)
 # Crossover, top 5 randomly select 2 partners for child
 for i in range(0, 5):
 for j in range(0, 2):
 # Create a child and add to networks
 temp = dynamic_crossover(pool[i], random.choice(pool))
 # Add to networks to calculate fitness score next iteration
 networks.append(temp)
# Create a Genetic Neural Network with optimal initial weights
gnn = GeneticNeuralNetwork(optimal_weights)
gnn.compile_train(10)
# Test the Genetic Neural Network Out of Sample
y_hat = gnn.predict(X_test.values)
print('Test Accuracy: %.2f' % accuracy_score(y_test, y_hat.round()))

遗传人工神经网络Python实现

遗传人工神经网络Python实现

结果

第一种模式:10代遗传算法和10个epochs的训练

第二种模式:10个epochs的训练

  • 遗传神经网络的测试准确度为 .96
  • 标准神经网络的测试准确度为 .57

遗传神经网络在相同数量的训练时期内将模型准确度提高了 0.39。

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